Sentence examples for by the quantization step from inspiring English sources

where represents the th quantization interval, determined by the quantization step and an offset angle.

where Q is determined by the quantization step size of the lossy coding in the base layer.

The robustness of the embedded watermark generally depends on the number of involved coefficients (i.e., l) and the embedding strength characterized by the quantization step size (i.e., ∆ k ).

The -factor was 200. 8 × 8 DCT coefficients are divided by the quantization step, which is generated by, where, and denotes a predefined quantization table and a -factor, resp).

They have observed that the shifted JPEG compression will introduce a Gaussian noise to each DCT coefficients and approximated the variance of the noise by the quantization step of the shifted compression.

Let us focus on one GNE p⋆, whose existence is ensured by Theorem 1, and let us suppose that p⋆ is such that p k ⋆ ≤ γ ⋆ / ( ν k ′ Δ ), where ν k ′ = ν k ( p ∖ k ′ ) is obtained using the vector p ∖ k ′ = Δ p ⋆ such that all components are scaled by the quantization step Δ, i.e., p k ′ = Δ p k ⋆.

This is due to the quantization noise (refer to earlier sections), and can be reduced by reducing the quantization step used in the watermarking procedure.

When fixing ρ t =16L (corresponding to PFA of 10−6), by adjusting the quantization step Δ, we obtained the watermarked images with the average PSNR of 42 dB, several examples of which are shown in Fig. 4. To assess the watermark imperceptibility, the MSSIM metric is adopted due to its compatibility with the human visual system.

The detection threshold ρ t is chosen based on the resulting probability of false alarm (PFA), and by adjusting the quantization step Δ, the watermarking image is made to meet a given objective image quality index, e.g., peak signal-to-noise ratio (PSNR), the mean structural similarity index (MSSIM) [19].

The range of QP values is defined from 0 to 51, and an increase by 6 doubles the quantization step size such that the mapping of QP values to step sizes is approximately logarithmic.

Furthermore, we assume that the quantization noise is a zero-mean random variable with the variance given by [7], where denotes the quantization step as illustrated in Figure 3.